Question

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 140°. Then angle BAC is equal to∶

• A. 38
• B. 40
• C. 50
• D. 60

Answer 1

Answer:

C. 50

 

ABCD is a cyclic quadrilateral with AB as the diameter of the circle.

∠ADC=140

∠ADC+∠ABC=180

∠ABC=180 −140 = 40

∠ACB=90 (angle subtended by a diameter at the circumference of the circle is 90)

In ΔABC we have,

∠ACB=90

∠ABC=40

∠BAC=180 − (∠ACB+∠ABC)

∠BAC=50